# Seminars & Events for Minerva Lectures

##### Inaugural Minerva Lectures I: Equidistribution

Equidistribution

##### Inaugural Minerva Lectures II: How to use linear algebraic groups

How to use linear algebraic groups

##### Inaugural Minerva Lectures III: Counting solutions mod p and letting p tend to infinity

Counting solutions mod p and letting p tend to infinity

##### Minerva Lectures I - The virtual Haken conjecture: An overview of 3-manifold topology

Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a

finite-sheeted cover which fibers over the circle. The first lecture will be an overview of 3-manifold topology in order to explain the meaning of Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory. The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory. The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special. Part of this result is joint work with Daniel Groves and Jason Manning. We will attempt to make these lectures accessible to a general mathematical audience at the level of a colloquium talk.

##### Minerva Lecture II - The virtual Haken conjecture: What is geometric group theory?

Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a

finite-sheeted cover which fibers over the circle. The first lecture will be an overview of 3-manifold topology in order to explain the meaning of Waldhausen's virtual Haken conjecture and Thurston's virtual fibering conjecture, and how they relate to other problems in 3-manifold theory. The second lecture will give some background on geometric group theory, including the topics of hyperbolic groups and CAT(0) cube complexes after Gromov, and explain how the above conjectures may be reduced to a conjecture of Dani Wise in geometric group theory. The third lecture will discuss the proof of Wise's conjecture, that cubulated hyperbolic groups are virtually special. Part of this result is joint work with Daniel Groves and Jason Manning. We will attempt to make these lectures accessible to a general mathematical audience at the level of a colloquium talk.

##### Minerva Lecture III: Geometric group theory and the virtual Haken conjecture

Waldhausen conjectured in 1968 that every aspherical 3-manifold has a finite-sheeted cover which is Haken (contains an embedded essential surface). Thurston conjectured that hyperbolic 3-manifolds have a

##### Minerva Lecture I: Sets with few ordinary lines

Given n points in the plane, an _ordinary line_ is a line that contains exactly two of these points, and a _3-rich line_ is a line that contains exactly three of these points. CLICK ON LECTURE TITLE FOR COMPLETE ABSTRACT.

##### Minerva Lecture II: Polynomial expanders and an algebraic regularity lemma

The _sum-product phenomenon_ is the observation that given a finite subset A in a ring, at least one of the sumset A+A or the product set A.A is typically significantly larger than A itself, except when A is "very close" to a field in some sense. CLICK ON LECTURE TITLE FOR COMPLETE ABSTRACT.

##### Minerva Lecture III: Universality for Wigner random matrices

Wigner random matrices are a basic example of a Hermitian random matrix model, in which the upper-triangular entries are jointly independent. CLICK ON LECTURE TITLE FOR COMPLETE ABSTRACT.